1. Field of the Invention
The present invention relates to an information processing apparatus, an information processing method, and a program product.
2. Description of the Related Art
Monte Carlo methods are widely used as calculating methods of VaR (Value at Risk, a percentile according to a confidence level α) of credit risk. Further, there are DM (Default Mode) method and MTM (Mark-to-Market/market price evaluation) method as methods of modeling credit risk. The DM method is a model creating a loss distribution using only the loss in the event of default, and is used for credit risk measurement for allowing credit, including medium and small companies and retails. On the other hand, the MTM method is a model creating a profit and loss distribution considering profit and loss other than in the event of default, and is used mainly for financial products (such as bonds for example) having a marketability that requires consideration of loss due to decline in market prices.
For either model of the DM method and the MTM method, methods of calculating VaR using a Monte Carlo method are known. For example, Japanese Laid-open Patent Publication No. 2009-32237 describes explanations of modeling of the DM method and the MTM method, and a calculating method of VaR with a Monte Carlo method. Further, besides Monte Carlo methods, for example, an approach to calculate VaR analytically with respect to the DM method is disclosed in “Analytical Evaluation Method for Credit Risk of Credit Portfolio Centered on Limiting Loss Distribution and Granularity Adjustment”, IMES Discussion Paper Series 2005-J-4, Institute for Monetary and Economic Studies, Bank of Japan, July 2005.
In late years, necessity of economic capital management (operating administration in the aspect of accounting management considering viewpoints such as what degree of risk, should be taken in what sector, profitability, and the like based on risk contributions of individual companies) is discussed both domestically and globally, and importance of breaking down the total VaR into “risk contributions of individual companies relative to VaR” is increasing.
However, in the above-described Monte Carlo methods, errors occur due to random numbers when calculating risk contributions, thereby causing problems such as unstable numeric values, discrepancy between the total VaR and the sum of the contributions of individual companies, taking a long time for calculation to obtain contributions in units which are too small, requiring a high-capacity memory, and so on.
On the other hand, there are proposed techniques to calculate VaR by an analytical approach. Using the analytical approach, it is possible to calculate risk contributions of individual companies accurately and rapidly. As described above, there are the DM method and the MTM method as methods of modeling credit risk, and the IMES Discussion Paper discloses an approach to calculate VaR analytically with respect to the DM method. On the other hand, the MTM method has many parameters as compared to the DM method and provides a complicated distribution, and thus has been considered to have a difficulty to calculate VaR analytically.
Now, the above-described problems will be described in more detail using drawings. FIG. 1 is a diagram representing rating transitions and losses of a obligor i by the DM method. Reference symbol pi denotes a default rate according to the rating of the obligor i. As illustrated in FIG. 1, in the DM method, ones other than default can be grouped together, and thus FIG. 1 can be expressed by a binomial distribution as illustrated in FIG. 2. FIG. 2 is a diagram illustrating an example of expressing FIG. 1 by a binomial distribution.
In the DM method, based on the rating transitions in FIG. 2, the probability distribution of loss in a portfolio is obtained as:
      L    =                  ∑        i            ⁢              L        i                        D      i        =          l              {                              x            i                    <                      θ            i                          }                        L      i        =                  D        i            ⁢              LGD        i            ⁢              EAD        i                        p      i        =          E      ⁡              [                  D          i                ]                        l              {        b        }              =          {                                    1                                              when              ⁢                                                          ⁢              b              ⁢                                                          ⁢              is              ⁢                                                          ⁢              true                                                            0                                              when              ⁢                                                          ⁢              b              ⁢                                                          ⁢              is              ⁢                                                          ⁢              false                                          where
L is a loss of the portfolio,
Li is a loss by the obligor i,
Di is a random variable indicating the status of the obligor i (default or non-default),
xi is a random variable indicating the enterprise value of the obligor i,
l[•] is a defined function,
pi is a default rate of the obligor i,
LGDi is a loss given default in exposure of the obligor i, and
EADi is an amount of exposure of the obligor i.
In practice, the default rate and the loss given default differ for every obligor included in the portfolio. Accordingly, even when an individual obligor can be expressed as in FIG. 2, the loss of the portfolio becomes a complicated probability distribution, for which it is not easy to obtain VaR.
Thus, conventionally, probability distributions and risk indicators (VaR) thereof have been calculated by simulation using a Monte Carlo method (generating random numbers corresponding to the random variable xi for the number of times of trial, and calculating in the order of Di→Li→L).
In late years, VaR calculating methods by analytical approximation such as granularity adjustment method have been known. Accordingly, it has become possible to stably and quickly obtain not only VaR but also risk contribution of each obligor.
            Risk      ⁢                          ⁢      contribution      ⁢                          ⁢      of      ⁢                          ⁢      a      ⁢                          ⁢      debtor      ⁢                          ⁢      i        =                  EAD        i            ⁢                        ∂          VaR                          ∂                      EAD            i                                    VaR    =                  ∑        i            ⁢                        EAD          i                ⁢                              ∂            VaR                                ∂                          EAD              i                                          
are an expression for obtaining the risk contribution of the obligor i when obtaining VaR analytically in the DM method, and an expression for obtaining VaR analytically in the DM method.
On the other hand, in the MTM method, the diagram representing rating transitions and profits and losses of the obligor i becomes a polynomial distribution similar to FIG. 3, in which the number of parameters per obligor becomes large as compared to the DM method. Thus, there is a problem that the analytical approximation of VaR becomes quite difficult as compared to the DM method. Here, FIG. 3 is a diagram representing rating transitions and profits and losses of the obligor i by the MTM method. Reference symbol pir denotes a rating transition probability of the obligor i from the current rating to the rating r.